What they are calling dimensional analyis is just the ability to convert from one set of units to another. A recommended way you do it is with "label factors". These are a series of multiplied conversion factors with labels on them, that get cancelled out in numerators and denominators until you get the units that you want.

For example

1.6 liters x 1000 cm^3/liter = 1600 cm^3

1600 cm^3 x (1 inch/2.54 cm)^3
97.64 in^3

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